score:5
The answer is no, Softbank doesn't have a monopoly. Telecom Square, literally the next shop over on Haneda's international arrivals floor, also sells voice & data prepaid SIMs on the Y!Mobile network, which is actually a Softbank subsidiary. The baseline price is higher but gets you more data, at ¥5500 for 1GB or ¥7500 for 3GB, plus unlimited local calls, valid for exactly 15 days.
Some rather bizarre catches:
I bought one anyway and, except for that annoying SMS thing, it worked just fine. Coverage and speed was decent too, even in the back blocks of Hokkaido.